Efficient Learning of Lattice Gauge Theories with Fermions

TL;DR

This paper presents a novel machine learning approach for determining parameters in lattice gauge theories, leveraging Schwinger-Dyson relations, applicable to complex models including QCD with fermions.

Contribution

It introduces a convex loss function framework based on Schwinger-Dyson relations, unifying and extending score matching for lattice gauge theories with fermions.

Findings

Applicable to gauge theories and Grassmann-valued fields

Extends to realistic lattice QCD models

Provides a new learning method for action parameters

Abstract

We introduce a learning method for recovering action parameters in lattice field theories. Our method is based on the minimization of a convex loss function constructed using the Schwinger-Dyson relations. We show that score matching, a popular learning method, is a special case of our construction of an infinite family of valid loss functions. Importantly, our general Schwinger-Dyson-based construction applies to gauge theories and models with Grassmann-valued fields used to represent dynamical fermions. In particular, we extend our method to realistic lattice field theories including quantum chromodynamics.